The invention relates to the measurement of stringed musical instrument vibrations and subsequent processing of these signals. More particularly, this invention relates to the reproduction of musical sounds characteristic of acoustic instruments into high fidelity electrical signals for amplification and reproduction of musical sounds, by uniquely exploiting, through measurements and subsequent signal processing the vector nature of string excitation forces (SEF) and body vibrations of stringed musical instruments (SMI""s).
Methods of amplifying (for purposes of both performance or recording) stringed musical instruments (SMI) employ sensors that measure acoustic pressure (i.e. microphones), force (i.e. piezo) and displacement (strain gauge, hall effect, laser), velocity (coil pickups) and acceleration (accelerometers). A common expectation in using techniques that combine sensors other than microphones is that the sensors will be mounted semi-permanently in a manner that mitigates sensor placement issues. While these sensors are obviously integral to electric guitars, players of acoustic SMI""s have grown to rely on the convenience and consistency of xe2x80x9cplugging inxe2x80x9d. In fact, acceptance of this technique has grown to the point that approximately 20% of acoustic guitars sold in the US have factory installed embedded sensor (ES) systems. We will refer to these sensors, along with any subsequent processing (analog or digital), as an embedded sensor technique in contrast to a solely microphonic approach.
Although microphones are by definition the only objective, quantitative means to directly capture the true acoustic sound of a SMI, microphone measurements of SMI sound are affected by placement and, in amplified scenarios, there is the potential for unstable feedback among microphone, instrument and the amplifier. To avoid problems of placement and feedback, embedded sensors such as piezo force transducers are often placed under the saddle of an acoustic guitar or on the bridge of violins and/or cellos. The quality of this amplified sound (typically taken from either bridge or sound hole based signals) has heretofore fallen short of the true acoustical signal measured from a microphone.
In striving to improve the reproduction of acoustic SMI characteristics using embedded sensor techniques, prior efforts have focused primarily on either of two distinct mechanisms involved in SMI sound generation. The first SMI characteristic is that the string force applied to the witness point (the point of contact between saddle and string) can be resolved into a plurality (up to 3) of significant components. Prior art teaches methods to isolate, suppress or advantageously combine string excitation force (SEF) components by improved sensor means. These efforts include U.S. Pat. No. 3,453,920 issued to Scherer, (xe2x80x9cScherer1xe2x80x9d) and U.S. Pat. No. 4,903,566 issued to Mcclish, (xe2x80x9cMcclishxe2x80x9d).
Lazarus U.S. Pat. No. 3,624,264 issued to Lazarus, (xe2x80x9cLazarusxe2x80x9d) aptly compares the motions of the bridge block of a guitar to those of a ship at sea; With the convention that the contact point of the guitar""s low E string is port, and the high E string starboard, the three acoustically significant modes of bridge block vibration (BBV) are pitch, roll and heave, Through proper positioning of vibration sensors about the bridge, works such as Lazarus or its commercial descendent Trance-Audio""s (xe2x80x9cAcoustic Lensxe2x80x9d) http://www.tranceaudio.com/manuals/lens.pdf and http://www.tranceaudio.com/lens.html), claim to effectively capture the tonal qualities of the SMI by indirectly measuring the multi-directional nature of SEF""s through measurements of BBV""s on the surface of the SMI. As shown below, while these sensors are responsive to the three vibration modes (pitch, roll and heave), the sound is primarily affected by repositioning the pickup on the body of the guitar and the ability to manipulate the sound is significantly constrained. Moreover, discussion below will describe the advantages of the present invention over limitations of sensor based component nulling techniques as represented by Scherer and McClish.
A second distinct SMI characteristic results from the structural features such as a resonant cavity that provide frequency responses unique to different classes of instruments. Embedded sensor approaches where sensors are directly responsive to the string excitation do not directly measure the characteristic colorations of an acoustic SMI. U.S. Pat. No. 4,819,537 issued to Hayes et al., (xe2x80x9cHayesxe2x80x9d) teaches a post-processing methods that can reintroduce the characteristic Helmholtz resonance of a particular SMI. Other ES sensor approaches, such as Lazarus and Trance-Audio, claim to be uniquely responsive to vibrational modes due to and representative of these characteristic resonances, but are limited to the sound that can be measured on the surface of the guitar. In contrast the present invention provides a capability and theoretical framework for more flexible manipulation of embedded sensor (ES) signals.
Moreover, a body of work (fairly represented by xe2x80x9cPlucked string models: from (Karplus-Strong) algorithm to digital waveguides and beyondxe2x80x9d, by M. Karjalainen and V. Vlimki and T. Tolonen Vol 22, number 3, Computer Music Journal, 1998, or http://www.acoustics.hut.fi/xcx9cvpv/publications/cmj98.htm) has developed synthesis techniques that combine multiple polarization string models with models of guitar body resonances.
These works contain a sophisticated theoretical basis for synthesis of a guitar signal, but in contrast to the present invention, do not teach the processing of embedded sensor signals that can re-create the sound characteristics of a particular SMI.
For analysis purposes, SMI vibrations are decomposed into modes that can be generally defined as having monopole, dipole or even quadrapole physical interpretations of distinct surface plate modal patterns, for example as taught by fletcher ((xe2x80x9cThe Physics of Musical Instrumentsxe2x80x9d) by Neville H. Fletcher and Thomas D. Rossing (Chapter 9) Springer Verlag ISBN: 0387983740). The representation of the SMI state by physical modes xcexa8i(r) is advantageous in the study of SMI acoustics, but another modal representation that is particularly suited to the simulation and re-creation of SMI acoustic characteristics (an objective of the present invention) involves xe2x80x9cPRISMxe2x80x9d modes. PRISM modes will be introduced by way of a description of a standard physical mode model of SMI sound generating mechanisms.
The distribution of surface state of a SMI (e.g. a guitar) can be described via a summation of modes:                                           α            ⁡                          (                              r                ,                w                            )                                =                                    ∑              i                        ⁢                                                            λ                  i                                ⁡                                  (                  w                  )                                            ⁢                                                Ψ                  i                                ⁡                                  (                  r                  )                                                                    ,                            (        1        )            
where xcexa8i(r) is the ith mode (r coordinates) linearly weighted and summed by the complex modal amplitude
xcexi(w)=ai(w)ejxcfx86i(W)xe2x80x83xe2x80x83(2)
(ai(w), "PHgr"i(w), magnitude and phase), to form the total state (displacement and or velocity) xcex1(r, w) as a function of frequency w and position r. The surface states xcex1(r, w) are then weighted and summed by the pointwise (with respect to r) acoustic transfer function C(r, w|R) to form the acoustic pressure
Smic(w)=∫C(r,w|R)xcex1(r,w)drxe2x80x83xe2x80x83(3)
seen at a point R as a function of frequency w.
Equation 3 defines the relation between physical state xcex1(r,w) and the output Smic(w), but more importantly for the present invention is the relation between the output and the particular physical excitation of this system which is the SEF vector                               F          =                      [                                                            V                                                                              T                                                                              L                                                      ]                          ,                            (        4        )            
whose vertical, transverse and longitudinal force components (all implicit functions of frequency) excite the heave, roll and pitch motions of the bridge block, which in turn excite unique combinations of the physical modes of an SMI xcexa8i(r). These combinations of physical modes can be regrouped into xe2x80x9cPRISM modesxe2x80x9d, which serve the role of a transfer function between the vertical, transverse and longitudinal force components of SEFs and their respective contributions to the acoustic pressure Smic(w) at point R.
Viewing the combination of the SMI""s physical response and the measurement system (microphone or other arbitrary linear device), Sq as a cascade of linear systems, and dropping the explicit notational dependence of xcfx89, we can recast the system model of equation 3 as a matrix product with input F, system model G and a generalized (one or more signals) output Sq as
Sq=Gq←FF,xe2x80x83xe2x80x83(5)
with individual elements defined by                               [                                                                      S                  1                                                                                                      S                  2                                                                                    ⋮                                                                                      S                  N                                                              ]                =                                            [                                                                                          g                                              V                        ,                                                  S                          1                                                                                                                                                g                                              T                        ,                                                  S                          1                                                                                                                                                g                                              L                        ,                                                  S                          1                                                                                                                                                                                g                                              V                        ,                                                  S                          2                                                                                                                                                g                                              T                        ,                                                  S                          2                                                                                                                                                g                                              L                        ,                                                  S                          2                                                                                                                                                          ⋮                                                        ⋮                                                        ⋮                                                                                                              g                                              V                        ,                                                  S                          N                                                                                                                                                g                                              T                        ,                                                  S                          N                                                                                                                                                g                                              L                        ,                                                  S                          N                                                                                                                                ]                        ⁢                          xe2x80x83                        [                                                            V                                                                              T                                                                              L                                                      ]                    .                                    (        6        )            
where gxcex7,Si(w) is defined as the transfer function between a particular SEF component xcex7 (xcex7⊂[V,T,L]), and the measurement Si. Equation 5, in its most general interpretation, relates the SEF force F, to a set of arbitrary measurements proportional to the forces applied to and vibrations on the SMI""s body. The superscript ( )q denotes a generic measurement scenario, employing a microphone or a set of embedded sensor, and is used in the discussion of general principals involving the present invention.
Consider the specific vector measurement of forces and vibrations from a set of sensors referenced to body points (bp) on the bridge block of an SMI, that responds to the SEF F in accordance with                               S          bp                =                              (                          [                                                S                  1                  bp                                ⁢                                  xe2x80x83                                ⁢                                  S                  2                  bp                                ⁢                                  xe2x80x83                                ⁢                                  S                  3                  bp                                            ]                        )                    T                                    (        7        )                                          xe2x80x83                ⁢                  =                                    G              i                              bp                ←                F                                      ⁢                          F              .                                                          (        8        )            
Without development at this point, we define a xe2x80x9csyntheticxe2x80x9d signal model where, contrary to the convention of the physical measurement systems of equation 5, the system transfer function uses an arbitrary set of ES measurements Sq (a generalization of Sbp) as an input to the system modeled by Gmic←q (as yet undetermined) to yield the output signal
Smicxe2x80x2=Gmic←qSq,xe2x80x83xe2x80x83(9)
where the modified superscript of Smicxe2x80x2 denotes the goal of synthesizing the original microphone phone signal Smic.
Equation 9 has the same form as the SMI signal model (equation 5) with inputs Sbp and output Smicxe2x80x2.
It will be readily seen that other signal data/re-creation pairs are achievable, for example:
1. Accelerometer to microphone:
acceleration measurements on the face or bridge block of the SMI are processed to recreate the SMI""s microphone outputxe2x80x94xe2x80x9cthe soundxe2x80x9d of the instrument.
2. Force measurement device to microphone:
force measurements on the bridge saddle interface of the SMI, are processed to recreate the SMI""s microphone outputxe2x80x94xe2x80x9cthe soundxe2x80x9d of the instrument.
3. Force measurement device to accelerometers:
force measurements on the bridge saddle interface of the SMI, are processed to recreate the accelerations on the SMI""s face.
4. Accelerometers to force measurement device
acceleration measurements on the face or bridge of the SMI, are processed to recreate the forces at the contact point R saddle interface of the SMI.
A key innovation of the present invention is the consistent means by which the full information content of the SEF components F is uniquely preserved throughout an arbitrary measurement, Sq and subsequent processing via Gmicxe2x80x2←q to enable all of the embodiments described above.
In a preferred embodiment of the invention, a plurality of sensors are mounted on one or more common mechanical bases onto a MI and processing this vector signal set in a systematic manner. The analog signals from these sensors are processed in either analog or digital (with prior conversion) formats by methodologies described herein to faithfully reproduce acoustic characteristics of the MI as could be measured by a microphone.
In SMI""s such as guitars, SEF""s are applied to the instrument""s face through a bridge and/or bridge/saddle combination where the string termination point is placed well within the bridge block. In other SMI""s such as jazz guitars and violins, strings are stretched over a bridge and/or bridge/saddle combination and terminate at a separate tailpiece. In this case the present invention defines a means to measure a SEF that more faithfully models the forces acting on the SMI.
The benefits of the present invention stem from the basic ability presented herein to decompose a set of sensor signals into their constitutive components and with a high degree flexibility, accurately and efficiently recombine these components. Preferred embodiments of the present invention provide advantages that include
the ability to faithfully resynthesize the SMI sound measured by a microphone with a set of ES sensors, which can be installed in a repeatable fashion to provide a microphone sound without the cost or complications of a microphone. Hence, the present invention defines and implements a means to re-create Sq through the set of re-creation filters Gmicxe2x80x2←q whose factored components include the SMI sound characteristic Gmic←F and the correction for measurement coloration Gq←Fxe2x80xa0. The pseudo-inverse operation ( )554  and its operation on the measurement coloration Gq←Fxe2x80xa0 will be explained below.
the ability to reapportion the longitudinal,vertical and transverse components of the SMI output. The phrase xe2x80x9clongitudinal component of the SMIxe2x80x9d meaning the component of the SMI output due to the longitudinal component of SEF F.
the ability to null specific SEF components (longitudinal,vertical or transverse) of the SMI output. For example it is well known that the longitudinal components of a vibrating string include harmonics that are twice the fundamental frequency of vibration. Removing these components without spectral filtering can provide an advantage in pitch detection application where these longitudinal modes are an unwanted signal characteristic.
the ability to isolate individual components of the SMI output due to longitudinal, vertical or transverse SEF components, for further nonlinear processing.
the ability to manipulate a two sensor system responsive to a plurality of SEF components as a subset of the full processing technique.
the ability to specify a new system response Gmicxe2x80x2←q that includes an arbitrary defined SMI characteristic Gmic←F xe2x80x9cgraftedxe2x80x9d onto the correction for measurement coloration Gq←Fxe2x80xa0.
An object of this invention is to provide a method of measurement and subsequent processing of musical instrument signals to faithfully reproduce existing acoustic musical instruments.
It is another object to provide a method of processing signals to systematically reproduce characteristics of xe2x80x9ctheoreticalxe2x80x9d acoustic instruments with arbitrary relation to existing SMI""s.
It is another object to provide a method of processing signals to systematically reproduce the total characteristics of the SMI/microphone combination by parametrically altering the system characteristics. For example, combinations of Prism modes can be interpreted as corresponding to distinct physical modes of vibration (e.g. monopole, dipole) whose sound radiation characteristics have physically predetermined variations due to the microphone""s distance to the SMI and it""s relative angle to the normal to the guitar""s surface. Parametrically linking the phase and amplitude of specific Prism modes to a microphone""s relative position, affords a means to programmatically control the position of a xe2x80x9cvirtualxe2x80x9d microphone.
It is another object to provide a method of processing signals to systematically null specific component(s) of the SMI microphone output, said component(s) being due to longitudinal, vertical and/or transverse SEF components.
It is another object to provide a method of processing signals to reapportion the longitudinal, vertical or transverse SEF components of the SMI output.
It is another object of this invention to provide an improved means of measuring Sq.
It is another object of this invention to determine the elements of the system model Gmicxe2x80x2←q which do not require specific knowledge of the underlying acoustic signal model Gmicf.
It is another object of this invention to process Sq via equation 9 to generate signals Smicxe2x80x2 that approximate a reference signal such as the microphone signal Smic.